Question

Show Intro/Instructions 5.35 Gaming and distracted eating, Part I: A group of researchers are interested in the possible effects of distracting stimuli during eating, such as an increase or decrease in the amount of food consumption. To test this hypothesis, they monitored food intake for a group of 44 patients who were randomized into two equal groups. The treatment group ate lunch while playing solitaire, and the control group ate lunch without any added distractions. Patients in the treatment group ate 52.1 grams of biscuits, with a standard deviation of 45.1 grams, and patients in the control group ate 27.1 grams of biscuits, with a standard deviation of 26.4 grams. Do these data provide convincing evidence that the average food intake (measured in amount of biscuits consumed) is greater for the patients in the treatment (solitaire, distracted) group? Assume that conditions for inference are satisfied. Use a 5% significance level. USE YOUR TI CALCULATOR What are the hypotheses for this test? O Ho: Hno distraction Ha: Pno distraction Hdistraction Hdistraction Ho: Pno distraction Ha: Mno distraction distraction distraction Ho: Hno distraction Ha: Pro distraction Hdistraction distraction The p-value for the hypothesis test is: (please round to four decimal places) Interpret the result of the hypothesis test in the context of the study: Do these data provide convincing evidence that the average food intake (measured in amount of biscuits consumed) is greater for the patients in the treatment (solitaire, distracted) group? Answer "yes" or "no" and explain how you came to your conclusion, referencing your p-value.

Answer 1

Solution:

We are given:

Ino-distraction = 27.1

Sno-distraction = 26.4

n = 22

I distraction = 52.1

-Sno-distraction = 45.1

n2 = 22

What are the hypotheses for this test?

HO: Mno-distraction = Midistraction

H : Pino-distraction < Medistraction

The alternative hypothesis is less than type because we have to test the average food intake (measured in amount of biscuits consumed) is greater for the patients in the treatment (solitaire, distracted) group.

The p-value for the hypothesis test is:

p - value = 0.0151

The steps to get the p-value using the TI-84 are:

Press STAT key and scroll right to TESTS.

Scroll down to 2-SampTTest..

Input: stats

Enter the values as:

2-SampITest Inpt:Data Stats SX18264 P1:72 KF > 2 Pooled: No Yes Calculate Draw

Press calculate and the output is given below:

11 2-SampTTest -II | 生... iPÜDIXIX

The p-value is given as p.

Interpret the result of the hypothesis test in the context of the study: Do these data provide convincing evidence that the average food intake (measured in the amount of biscuits consumed) is greater for the patients in the treatment (solitaire, distracted) group?

Yes. Since the p-value is less than the significance level 0.05, we, therefore, reject the null hypothesis and there is sufficient evidence to conclude that the average food intake (measured in amount of biscuits consumed) is greater for the patients in the treatment (solitaire, distracted) group

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